Research and Development Laboratories of the Portland Cement Association RESEARCH DEPARTMENT Bulletin 66 Effect regate on Shrink- Concrete and Hypothesis Concerning Shrinka GERALD PICKETT February, 1956 CHICAGO Authorized Reprint of a Copyrighted OUBNAL OP THE AMERICAN CONCRETE INSTITUTE 18263 W. McNichoIs Rd., Detroit 19, Michigan January 1956; Proceedings Vol. 52, p. 581 Title No. 52-36 Effect of Aggregate on Shrinkage of Concrete and a Hypothesis Concerning Shrinkage By GERALD PICKETTt SYNOPSIS A theoretical formula is derived for effect of aggregate on shrinkage of con- crete during drying. Experiments designed to test the validity of the formula tic reported. In addition to indicating the validity of the formula, the data give the follow- ing indications: (1) First shrinkage is greater than an\ subsequent expan-mu or shrinkage resulting from moisture change. (2) At a given aggregate con- tent the shrinkage is approximately proportional to water-cement ratio (3) Alter hist shrinkage, subsequent volume changes are approximately inde- pendent of water-cement ratio. (4) When shrinkages ol specimens of the higher water-cement ratio are plotted against the square root of period of <lr\ ing, the shapes of the curves for second shrinkag( re appreciably different from those for first shrinkage in that they have considerable curvature uear the origin. An explanation of these effects is given. INTRODUCTION A number of years ago, while at the Portland Cement Assn., the author arrived al a theoretical formula for effect of aguregate on shrinkage of con- crete or mortar during drying. Experiments designed to test the validity of the formula gave results that were in fair agreement with the formula. How- er. certain factors in the formula which should depend on properties of the p te varied with conditions of drying and therefore led to the conclusion that the hydrated paste did not always have the same properties. The pur- p , this paper is to present the theoretical formula, experimental results thai were obtained, and speculations in regard to the paste that resulted from i Btudy of the data. DERIVATION OF FORMULA In deriving the formula, consideration is first given to effect on shrinkage of one small, spherical particle of aggregate in a large body of concrete, the surrounding concrete considered to he a homogeneous material. This ap- proach is similar to that of Guth 1 and Dewey,* who were concerned with the effect of fillers on elastic properties. The restraining effect <>f aggregate ♦Received by the Institute Mar. 17. 19o4. Title No. 52 ifl a part of c ?hted Journal of tiif. American Concrete Institute. V. 27, No. 5. Jan. 1956. Proceedings V. 5-' -parate prints are availa bi oO cents each. DiicuMion (copies in triplicate) should reach the Institute not later than May 1. 1956. Address 18. McNicnola tlflember American Concrete Institute. Guest Professor of Civil Engineering. Bengal Engineering College, West Bengal, India. 581 582 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1956 on shrinkage of concrete was pointed out by Carlson.' On the assumption that both the particle and the rest of the body are elastic, an expression is derived lor reduction in over-all shrinkage of the body due to the one small nonshrinking particle. This provides a formula for the effect of adding each subsequent particle if the body including all particles added previously is assumed to be homogeneous. This formula is then expressed n, differential equation form and an integration made to obtain the final formula. It will be expedient to consider that the small, spherical particle is at the center of the body of concrete which is also a sphere. If the particle is small compared to the shortest distance from it to the concrete surface, no great error will be introduced by treating the concrete as spherical with a radius equal to that distance. The restraint of the small sphere as the large sphere tends to ink will cause the following stresses in the large sphere. 4 :i pa 3 b 3 — r Cr = ~ T 3 " b 3 - a* (1 pa 3 b 3 + 2r 3 (2) 2 r 3 53 _ a 3 where <r r = normal si ress in the radial direction a t = either oi two normal stresses pei prndicular to the radius r = radial coordinate a = radius of inner sphere b = radius of outer sphere p = unit pressure between inner and outer spheres Under these conditions of spherical symmetry, radial displacement 5 of any point in the outer sphere caused by the restraint of the inner sphere, ana referred to the unrestrained position, is r (3) (1 — /z) <*t — M°> where E and M are Young's modulus and Poisson's ratio, respectively, for the outer sphere. FromEq.(l), (2), and (3) pa 3 \~l ~ m *> 3 + 2r 3 , 6 3 - r e7* 5 - 2 b 3 - a 3 + M b 3 - a J (4) Airlrb The restraint of the inner sphere has reduced the volume shrinkage of the total body by the amount = -fe^Z ( l - ^ db * (5) r = b E \ 2 )b 3 - a 3 where AV = 4/3 ira 3 is the volume of the small sphere. If the restraint had not been present, the body would have reduced in volume by 3SY, where V is its total volume and S is the unit linear shrinkage. The reduction in volume shrinkage will therefore be designated as - 3a£1 , or - 3 A SV = - (6) E \ 2 / b 3 - a 3 Another expression containing the pressure p will be found by considering the compressibility of the restraining particle. Reduction in volume of the EFFECT OF AGGREGATE ON SHRINKAGE 583 particle caused by pressure p on it will be equal to the reduced space avail- able to it within the larger body, or 1 - 2 M .>i>± V = 35 ^V - 4tt«-5 *. 7) r = a where E g and p g are the elastic constants of the particle and 8 is given by Eq. (4). Eliminating p between Eq. (6) and (7) and setting b/a = oo gi\ e- 31 I - M I (8) I + m + 2i I - 2»,)E/E I (9 >• ting l> <i = co will introduce an error especially for particles close to the surface. However, it is believed that this error is not relatively as important as other* entering this derivation. Lei volume of aggregate per unit volume of mix be g; then the increase in g due to the addition of one particle of volume A V to tin; mixture will be gV + AV AT Afl - ; — — -- - g = (1 - g) V + Al * v "' I + Al (10) From Eq. (8) and (10) &<s «ak r + a i S 1 - g or, m differential form, (II ' S 1 - 12) The t i tor a is probably a function of y since the elastic constants ot the mixture. E and /x, may depend on g. But if a may be considered to be inde- pendent of <7, then Kq. (12) integrates to 8 - So(l - u) a (13) where So is the shrinkage that would occur if no aggregate wrere pr< >nt I or later use this equation may be written in the form . ,s '° . l hi = Of log S * 1 - § 14 TESTS To test the validity of the formula. 1 x ^ x llj^-in. prism- were prepared with various percentages of aggregate ranging from percent to about 70 percent by volume. Three different types of aggregate (pulverized silica, standard < >t!awa sand, and graded Elgin sand) were used to determine whether size and gradation of aggregates would also be an appreciable factor. Two nts. a high-early-strength and a normal, and two water-cement ratios were used to determine in what way the effect of aggregate might be in- fluenced by type of cement and water-cement ratio. 584 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1956 TABLE 1— GENERAL OUTLINE OF CONDITIONS IN STUDY* Later it was decided to investigate reversibility of volume changes of the- i6ed Percent apgrega- bv abso- lute voluniet Hiiih-earl ica flour Standard Ottawa Ln mix sand Gr .1 I Band I ! 5 15 30 specimens. For this purpose specimens were alternately submerged in water iht an d dried in air. Each drying was w/c b\ end for °| Id was inw ftd-forn _ry 5 , :it r,ha, newat <> r 1 at ?~, . an( j , i • ;iod was M .1 T ,. M were n.ade devia- ns fr 05 at 50 percent relative humidity for at 035 least 224 days and each period of wet- ting was si day-. This work was be- guo in January, L942, and continued for about 2 year-. Table 1 gives the general outline of conditions covered in the study. Miv - containing up to 5 percent t«;<i re gate were too wet and those with mor< ■ • toodrj foi preparation of reasonably homogeneou ] , ted n d of the position of the molds dun... setting some eft, ..i bleeding but many of the wet mixes were LU6 eoi thecoml ed effects of bleeding, shrinkage m absolute periodic turning i tb molds- Some drj mixes bad high , ,1 g h in most cases percentage oi air w kept low by , >u8t an The wid< mg in plastic properties ol the mixee may ... mii iiti< in results. S hri nk , ng drying I - sion duriw wetting for the specimens , | . t, . , , ,t are show., graphicallj in Fig I and 2 ,1, , with normal a ment but are not shown. hrii ir }, curv< ras - stimated. Tin n suits are I le ' i 111 ni . - I i </ were rciputed from Tal 2 V to Eq n the ta hould b repr< t lii ii tl i " The data foi W/C ■ ,11 i, ; ight line with a slope a eq d tanta in Eq. (9 would ma I 7 , m n that w ild gi i thi> value i* - 0.21 1). w/C • 0.50 'i ell •■' it w • j h } \u a >1« 1.7 P ■ li liefartl >m the tin* , ben < >ntai d a consid ibk pen 1 1 1 1 ■ « li r ' v. j I j ,d< i ih« d formul a. ..,i. in ! i linkage < ■ iiH EFFECT OF AGGREGATE ON SHRINKAGE 585 Other ideas suggested by the data In addition to indicating the validity of the formula for the effect of assresate on shrinkage, the data give the following indications: (1) Fir>t shrinkage is greater than any subse- quent expansion or shrink- age. (2) At a given aggre- gate content first shrink- age is approximately pro- portional to water-cement ratio. (3) After first shrinkage, subsequent vol- ume changes are approxi- mately independent of water-cement ratio. (4) When shrinkage of speci- mens of the higher water- cement ratio is plotted against the square root of period <>i drying, the shape- of the curves for second shrinkage are appreciably different from those for first shrinkage in that they have considerable curva- ture near the origin. In general these four indications were either not xpected or not expected to the degree indicated by Fig. I and 2. Some of the change in behavior might have been due to carbo- nation during the first dry- ing period, but the major change is believed due to other causes, as will be discussed below. i r *■" -5 J* Shr -■ i rgofc A jg-e ggte . palverrzea $>?c<2 w J. 50 Secona Expansion Square root of dau,s exposed Q a £ SCOC i » Si S* <oge _0% aggregs+e 5" - * a so^d *v E - Secona Sfi' nkage if • G 14 2 4 & 9 \2 14 2A6G 0:4G8 Square root cf days exposed c o ^ 5000 c ■ t i— — « — r v St Shrink e OXpggregcte El gin sand . • 0.50 Second kage Second E.xpanS'Q* 2 4 2* 2 4- S G 10 12 14 Square root of days exposed 6 a Fig. 1 — Shrinkage during drying and expansion during wetting for pulverized silica, Ottawa sand, and Elgin sand using high-early-strength cement and W C = 0.50 586 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1956 1 —I » T 1 T— T t r I « * 6000 ■♦- c o - sooo Pulverized silica f/rsf Shrinkage 0% aggregate First . Expansion Second Shrinkage Second Expansion o— *-* « * » a $ E 4 6 ^ * ♦ « • » " 3 2 « « • Square root of days exposed t/> c 6000 O £ 5000 c o) 4000 c u X 3000 c u T r t 1 r 1 r 1 r Ottawa sand w/c * a 35 st Shrinkage c 2000 1000 0% aggregate —S.9% f -3% Expansion Second kage Secono Expansion-! 6 10 12 14 Z 2 4 6 6 Square root of days exposed z 4 6 6 v» 1 1 t 1 T P T f ' P .9 5000 1 •£ 4000 w/c ' a 3s c X u c u 3000 Z000 1000 First Shrinkage q% aggregate HAIL F ' rSt _„_ 6 * Expansion Second ' nnuaae Secor t> portion C Z 6 Square root of days exposed Fig. 2 — Shrinkage during drying and expansion during wetting for pulverized silica, Ottawa sand, and Elgin sand using high-early-strength cement and W C = 0.35 HYPOTHESIS ON GEL STRUCTURE As a basis for an expla- nation it is proposed (1) that during first shrinkage some adjacent particles of the cement gel move closer together, whereas others move farther apart, and (2) that, in general parti- cles that have once made close contact will not re- turn to their original rela- tive positions with sub- sequent wetting. No definite picture of gel structure before fir shrinkage is required for this analysis except that the gel be slightly altered by the first shrinkage. As water is removed, inter- particle forces will change, necessitating relative movements between parti- cles for equilibrium of indi- vidual particles, [f thes< relative movements for each pair of particles are not in proportion to the original distances between their centers, the arrange- ment will be ni idered to have changed. If only discrete colloidal were present, of hydra ted cement might be mor- nearly like that of soil and show a shrinkage limn particles shrinkage EFFECT OF AGGREGATE ON SHRINKAGE 587 TABLE 2 FREE SHRINKAGE OF SPECIMENS OF VARIOUS PERCENTAGES OF AGGREGATE Absolute volume of aggregate per mix volume Shrinkage in imlhunths First shrinkage Second shrinkage Silica Ottawa sand Elgin sand Silica Ottawa sand Elgin sand W/C = 0.50 5870 5870 5870 2180 2180 2180 0.05 4000 5450 5350 17 JO 2100 2100 0.15 3600 4500 3720 1.530 1600 1500 0.30 2200 2850 2700 950 1100 1100 0.50 _'( >00 1700 1650 710 670 640 0.67 m— 890 ^^^™ ^^■^^ 410 W C = 0.35 3700 3700 3700 2050 2050 21 '.".0 0.06 3230 3450 3380 1700 1750 0.18 2410 2720 2690 1300 1 380 1430 0.34 — 1800 1810 — moo 1000 0.53 \*W 1080 — ">10 620 0.62 900 300 i.e., down to some limiting shrinkage, it would show a shrinkage in volume i-ninparable to the volume of water lost. However, in concrete, restraining bodies act from the beginning of drying to reduce shrinkage. 3 The restrain- ing bodies are the aggregates, unhydrated cemenl grains, and staUe micro- crystalline products of hydration. There would, of course, be some differ- '/> o . I 0.8 _ C-6 0.4 0.2 - 3.0 _D 0.0 loq§2 = a\oq . — 0C=I.7- A / w/c=0.35 • - l st Pulverized Silica O - 2 nd n •' A - i st Ottawa Sand A - 2 nd l% • » - 1 st Elgin Sand n - 2nd h « 0.2 0.4 0.6 0.0 0-2 0.4 0.6 0.8 og i-g Fig. 3 — Effect of aggregate on shrinkage 588 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1956 ence in the intrinsic shrinkage of cement gel and soil because of the bonds between p'-l particles. Experiments show that concrete shrinkage instead of being about equal to volume of water lost is ordinarily only about 2 to J per- cent as much. When shrinkage is not equal to loss of water, .space. will form and hydrostatic tension must result, A given ge particle will be under tensile for, ,. tending to pull it toward adjacent particles These forces may be intense, as is shown below by the relation between hydrostatic tension and relative humidity. Under the conditions for which Kelvin s equation for the curvature of a meniscus in equilibrium with its vapor applies, the intensity ot hydrostatic tension of water at room temperature is given by r = - 19,600 log, h where T = hydro 'tic tension in psi h = relative humidity For example, if h = 0.98, T = 392 psi and if h = 0.50, T = 13,600 psi. Kelvin's equation probably is not applicable when radius of curvature is onlv a few molecular diameters. Under the action of forces of hydrostatic origin some adjacent particles will U pulled or pushed closer together while other adjacent particles will be pull, farther apart. As two adjacent particles are brought closer together, large compressive forces at the points of closest approach will naturally arise from inter molecular repulsion. These compressive forces should in- crease with increase in nearby tensile forces so that the particle, remain m equilibrium. As a result of high contact pressures, the particles will probablv develop chemical or surface bonds which will tend to prevent future separation of particles, even after hydrostatic tension has been decreased by increase in water content. The above considerations lead to the conclusion that the first shrinkage al- tei s gel structui so as to change size distribution of spaces between partial Larger sp es will become larger and smaller ones will become smaller De- nse in general those particles that were closest to each other are brought even Los< r together and those particles that were separated by larger spaces are p lied farther apart. In this analysis it is not necessary to decide whether the spaces under consideration are the capillary spaces or the much smaller gel pores or both. If the spaces are capillary spaces, then the word ''particle" refers to the capillary walls rather than to individual gel particle,. Application of the hypothesis to test results The first shrinkage is greater than any subsequent expansion or shrinkage (indi. tion 1. p. 585) because the arrangement of gel particles and groups oi gel particles is changed during first shrinkage. At a given aggregate content the extent of first shrinkage should increase with increase in water-eemen rati«» indication 2. p. 585). The original spacing of cement grains depend on the water-cement ratio and therefore th< iverage spacing of the gel ir- ticles in their first arrangement should al,o depend on water-cement ratio. Mon motion during first shrinkage is possible with greater spacing. EFFECT OF AGGREGATE ON SHRINKAGE 589 After the first shrinkage subsequent volume changes are approximately in- dependent of water-cement ratio (indication 3, p. 585) because after once having been dried the spacing between adjacent gel particles should be more a function of humidity and of the corresponding degree of drying than of origi- nal spacing. The gels from mixes of higher water-cement ratio will have a more open structure between agglomerations of particles but not necessarily any greater capacity for changes in volume. This last statement is in accord with the conception of gel structure given by Powers. On the basis of various experiments he concludes that the gel substance has a characteristic spacing of the gel particles. 56 - 7 The difference in shape of the curves for first and subsequent shrinkages (indication 4, p. 585) is attributed to both the change in distribution of cap- illary sizes and to the fact that stabilization takes place during first shrink- age but does not occur appreciably during subsequent shrinkages. In any given region in the specimen most of the water in the larger capillaries must be lost before appreciable hydrostatic tension can be developed. During the first shrinkage, before gel structure has become stabilized, appreciable shrinkage can take place with little hydrostatic tension. But after the gel lias become stabilized, larger interparticle forces are required to produce comparable shrinkages. The pastes of lower water-cement ratio do not have many large capillaries and therefore, in drying, soon reach the linear portion of the shrinkage versus square-root-of-time relation even though the gel has been stabilized. Moreover, the gels in pastes of low water-cement ratio undergo relatively little structural change during first shrinkage because of the original close particle spacing. From the above picture it would appear that all volume changes after the first shrinkage should be fairly reversible; however, shrinkage stress- result- ing from nonuniform drying or wetting and chemical changes will no doubt cause some change in the structure and therefore prevent complete reversi- bility. Explanation of plastic properties of hardened concrete As noted by many investigator concrete has the capacity for a com- paratively large amount of creep and the apparent rate of creep for a given stress is relatively large if loads are applied during drying. Although an attempt was made in an earlier paper 8 to show that at least a part ot this effect was a natural consequeme of nonuniform shrinkage and a nonlinear stre,s-creep relationship, no satisfactory explanation has been given for the large capacity for creep without failure in tension (cracking) that concrete has while drying as compared to its smaller capacity for creep before or after drying. By assuming that gel particles change their relative positions, some making closer contacts and others separating during drying, we can understand the large capacitv for creep which concrete has while drying. The picture is that each small community of particles will undergo considerable distor- 590 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1956 tional deformation. However, because these deformations are miscellaneously orientated, a region consisting of many such small communities will ap- parently have no distortion. But if a small stre in a given direction is added, the region will have a resultant distortion which could be of con- siderable magnitude if high interparticle stresses are also present. After the gel particles have acquired stable positions, the rate of creep will be much less for a given stress and the capacity for creep will be materially reduced, for the action just described cannot take place. ACKNOWLEDGMENTS Except for minor revisions, this paper was written in 1944 while the author was at the Portland Cement Assn. working under the direct supervision of T. C. Powers. Credit is due Air. Powers and' the Portland Cement Assn. not only for the work here reported but for urging that the paper be submitted lor publication. REFERENCES 1. Gutli. E., 'Theory of Filler Reinforcement," Journal of Applied Physics, V. 16, Jan. 1945, p. 20. 2. Dewey, J. M., "Elastic Constantsof Materials Loaded with Xon-Rigid Fillers,' 1 Journal of Appl I Physics, Y. 18, June 1947, pp. 578-581. 3. Carlson, l: W., Drying Shrinkage of Laiu<' Concrete Members," ACI ■!"• enal, .Jan - 1 t>. L937, Proc. V. :«, \>. -. I. Timoslu ■), S., and Goocli I \'., Theonj of Elasticity, 2nd Edition, McGraw-Hill Book Co., Inc.. \ T ew York. L951, p. 359. 5 Powers, T. C, and Brownyard, T. L., "Physical Properties of Hardened Portland Cem. ,,t Paste,' ACI Journai . Feb. 1947, Proc. V. 43, pp. 495 and 704-7(M>. 6. Powers, T. C, \ Working Bypothesis for Further Studies of Frost Resi>i:mce of Con- r VCIJ cjrnal, Feb. 1945, Prac. V. 41, p. 246. 7 Powers, T. C, and Helmutli II \., "Theory of Volume Chang' - in Hardened Portland Cement Pas 1 i luring Freezing Proceed is, Highway Research Hoard, V. :\2, L953, p. 285. 8. Pickett, G., 'I be Effect oi Moisture Content on the Creep of Concrete under a Sus- tained I l \CI Joui w,, Feb. 1942, Proc. V. 38, p. 333. For such discussion of this paper as may develop please see Part 2, December 1956 Journal. In Proceedings V. 52 discussion immediately follows the June 1956 Journal pages. Bulletins Published by the Research Department Research and Development Division of the Portland Cement Association Bulletin 1 If Estimation of Phase Composition of Clinker in the System SK) 2 -2CaO SH):-3CaO AM> 3 -4CaO AU0 3 Fei0 3 at Clinkering T attires," bv L. A. Dahl, May, 1939. ■v, o. .., *i **\ if. \r.. 11 I'). 1 3CaO Temper- Reprinted from Rock Products, 41, No. 9. 48; No. 10, 46; N (1938J; 42, No. 1, «8; No. 2, 46; No. 4, 50 (1939). 11, 42; No. 12. 44 Bulletin 2 Bulletin 3 "The Bleeding of Portland Cement Paste, Mortar and Concrete Treated as a Special Case of Sedimentation," by T. C. Powers; with an appendix by L. A. Dahl; July, 1939. -"Rate of Sedimentation: I. Nonflocculated Suspensions of Uniform Spheres; II. Suspensions of Uniform-Size Angular Particles; III. Concentrated Flocculated Suspensions of Powders ; by HAROLD H. Steinour, October, 1944. Repi inted from Industrial and Engirt Chemistry, 36, 018, 840, 901 (1944). Bulletin 4— "Further Studies of the Bleeding of Portland Cement Paste," b> 11 vitoi i> H. Steinoi k, December, lul.">. Bulletin 5 Bulletin 5A Bulletin 6 Bulletin 7 Bulletin 8 Bulletin 9 Bulletin 10 Bulletin 11 "A Working Hypothesis for Further Studies of Frost Resistance of Concrete," bv T. (.'. POWERS, February, U»4. r >. Reprinted from Journal of the American Concrete Inetitute (February, 1045); Pro- ceeding* 41, 245 (1945). Supplement to Bulletin 5; Discussion of the paper "A Working Hy- pothesis for Further Studies of Frost Resistance of Concrete, by T C Powers; discussion by: Ruth D. Tbrzaghi, hm ,,, as M. Henry, H W Brewer, A. R. Collins, ami Author; March, 1946. Reprinted from Journal of the American Co He Inst, t Supplement (November 1945); Proceedinus, 41. 272-1 L945). "Dynamic Testing of Pavements," by Cerai u Pl< mm. ^pril, 1946 Uepri..te<l fro.,. Journal of the American C rete Instituti April. 1945); Proceeding*. 41, 473 (1945). -Equations for Computing Elastic Constants from F, * xu /^*£* tor- sional Resonant Frequencies of Vibration of Prisms and Cylinders, by Gerald Picxett, September, 194;). Reprinted from Proceedings, Am, eon Society for 3 ling M atenah 45,848 194 discussion, 864. -"Flexural Vibration of Unrestrained Cylinders and Disks," bv Gerald Pkkett, December, 1 ( .)4">. Reprinted from Journal of Applied Physics, 16, 820 1 1945). --Should Portland Cement Be Dispersed?" by T. C. Powers, February, 1 ( )40 Reprinted from Journal of the Am an C rete Ins* November. 1945); Pro- ceedings,^, 117 (1946). -"Interpretation of Phase Diagrams of Ternary Systems," h> L, A. Dahl, March, 1946. Reprinted from Thi Journal of Physical Chemistry, 50, M (1946). --Shrinkage Stresses in Concrete: Part l-Shrinkage or Swelling Its Effect upon Displacements and Stresses in Slabs and Beams of Homogeneous, Isotropic, Elastic Material; Part 2 -Appl.ca .on of he Theory Presented in Part 1 to Experimental Results ; bv GBHALD Pickett, March, 1946. Reprinted from Journal of the American Concrete Institute January and February, 1946); Proceedinge, 42, I- (61 (1946). Bulletin 12 Bulletin 1£ Bulletin 14 Bulletin 15 Bulletin 16 Bulletin 1 ~ Bulletin I Bulletin 19 Bulletin 20 Bulletin 21 Bulletin 22 Bulletin 2 Bulletin 2 Bulletin 25 "The Influence of Gypsum on the Hydration and Properties of Portland Cement Pastes," by William Lerch. March, 1946. Reprinted from Proceedings. American Society for Testing Materials, 46. 1251 (1946). "Tests of Concretes Containing Air-Entraining Portland Cements or Air- Entraining Materials Added to Batch at Mixer," by H. F. Goxxer- iian, April, 1947. Reprinted from Journal of A xer. i Concrete Institute (June. 1944': Proceedings, 40 477 (1944 ; also supplementary data and analysis, reprinted from bupplement (November. 1944 ; Proceedings. 40. 508-1 <1944). "An Explanation of the Titration Values Obtained in the Merriman Sugar-Solubility Test for Portland Cement," by William Lerch. March. 1947. Reprinted from ASTM Bulletin. No. 145. 62 March. 1947). "The Camera Lucida Method for Measuring Air Voids in Hardened Concrete," by George J. Verreck. May, 1947. Reprinted from Journal of American Concrete Institute (May. 1947); Proceedings, 43. 1025 (1947). "Development and Studv of Apparatus and Methods for the Determina- tion of the Air Content of Fresh Concrete," by Carl A. Menzel, May. 1947 Reprinted from Journal of the American Concrete Institute (May, 1947 ; Proceedings. 43, 1053 (1947). "The Problem of Proportioning Portland Cement Raw Mixtures: Part I— A General View of the Problem; Part II— Mathematical Study of the Problem; Part III— Application to Typical Processes; Part I\ — Direct Control of Potential Composition"; by L. A. Dahl, June, 1947. Reprinted from Rock Products. 50. No. 1 109; No. 2, 107; No. 3. 92. No. 4. 122 (1947). "The System CaO-SiO.-H O and the Hydration of the Calcium Sili- cates," by Harold H. Steixolr, June, 1947. Reprinted from Chemical Reviews, 40. 391 T'47). "Procedures for Determining the Air Content of Freshly-Mixed Con- crete by the Rolling and Pressure Methods," by Cam V. Menzel, June, 1947. Reprinted from Proceedings. American Society for Testing Materials. 47, 833 <1947). "The Effect of Change in Moisture-Content on the Creep of Concrete under a Sustained Load," by Gerald Pi< kett, July, 1947. Reprinted from Journal of the American Concrete Institute (Februar\. iy42); Pro- ceedings. 38, 333 (1942). Effect of Gypsum Content and Other Factors on Shrinkage of Concrete Prisms,'* by Gerald Pickett, October, 1*47. Reprinted from Journal of the American Concrete Institute (October. 1947); Pro- ceedings, 44. 149 (1948). Studies of the Ph\sical Properties of Hardened Portland Cement Paste," by T ( . Powers and T. L. Brown yard, March, 1948. Reprinted from Journal of the American Concrete Institute (October-December. 1946; January-April. 194 1 ; Proceeding -H. 101 24'». 469, 549, 669. 845, y33 1 1947). "Effect of Carbon Black and Black Iron Oxide on Air Content and Dura- bility of Concrete," I y Thomas G. Tayi.or. May, 1*.*4S. Reprinted from Journal of thf A m Concrete Institute (April, 1948); Proceeding*, 44, 613 (1948 Effect of Entrained Air on Concretes Made with So-Called Sand- Gravel' Aggregates/' by Paul Klieger, November, 1 ( j48. Reprinted from Journal of the American Concrete Institute (October. 1948 » Pro- ceedings), 45, 149 1949). 4 A Discussion of Cement Hydration in Relation to the Curing of Con- crete/' by T. C Power- August, 1948. Reprinted from Proceedings of the Highway Research Board, 27, 178 (1947). Bulletin 2t> i . 1 'Long-Time Study of Cement Performance in Concrete/* This bulletin comprises four installments of the report of this investigation, by F. R. McMillan, L L. Tyler, W. C Han-en. William Lerch, C. L. Ford, and L S Brown. August, 1948. Reprinted from Journal of the Amerxcan Concrete Institute February-May. 1948 Proceedings . 44. 441 553 743. 877 (1948). 27 Bulletin 28 Bulletin "Determination of the Air Content of Mortars by the Pressure Method," by Thomas G. Taylor, February, 1949. Reprinted from ASTM Bulletin, No. 155. 44 (December. 1948). "A Polarographic Method for the Direct Determination of Aluminum Oxide in Portland Cement," bv C. L. Ford and Lorratne Le Mar, April, 1949. Reprinted from ASTM Bulletin, No. 157, 66 (March. 1949). "The Nonevaporable Water Content of Hardened Portland-Cement p aste — Us Significance for Concrete Research and Its Methods of Determination," by T. C. Powers, June, 1949. Reprinted from ASTM Bulletin, No. 158. 68 (May. 1949). Bulletin 30— "Long-Time Studv of Cement Performance in Concrete— Chapter 5. Concrete Exposed* to Sulfate Soils," by F. R. Mi Millan, T. E. Stanton. I. L. Tyler and W. C. Hansen, December, 1949. Reprinted from a Special Publication of the American Concrete Institute (1949). "Studies of Some Methods of Avoiding the Expansion and Pattern Cracking Associated with the Alkali-Aggregate Reaction," by William Lerch, February, 1950. Reprinted from Special Technical Publication No. 99, published by American Society for Testing Materials (1950). Bulletin 31 Bulletin 32 Bulletin 33 "Long-Time Study of Cement Performance in Concrete— Chapter 6. The Heats of Hydration of the Cements," by George J. Verbeck and Cecil W. Foster, October, 1949. Reprinted from Proceedings, American Society for Testing Materials, 50, 1235 (1950). "The Air Requirement of Frost-Resistant Concrete," by T. C. Powers; discussion bv T. F. Willis. Reprinted from Proceedings of the Highway Research Board, 29, 184 (1949). Bulletin 34 t * Bulletin 35 Bulletin 36 Bulletin 37 "Aqueous Cementitious Systems Containing Lime and Alumina, by Harold H. Steinour, February, 1951. "Linear Traverse Technique for Measurement of Air in Hardened Concrete," by L. S. Brown and C. U. Pierson, February, 1951. Reprinted from Jovrnal of the American Concrete Institute (October, 1950); Proceed- ings, 47, 117 (1951). "Soniscope Tests Concrete Structures," by E. A. Wmitbhi rst, February, 1951 Reprinted from Journal of the American Concrete Institute (February, 1951); Pro- ceedings 47, 433 (1951). "Dilatometer Method for Determination of Thermal Coefficient of Expansion of Fine and Coarse Aggregate," by Georoe J. Verbeck and Werner E. Hass, September, 1951. Reprinted from Proceedings of thi Highway Research Board, 30, 187 (1951). Bulletin 38-"Long-Time Study of Cement Performance in Concrete— Chapter 7. New York Test Road," by F. H. Jackson and I. L. 1 tler, ( tetober, 19ol. Reprint* <1 from Journal of the American Concrete Institute (June. 1951 Proeeedxngt 47, 773 (1951). "Changes in Characteristics of Portland Cement as Exhibited by Lab- oratory Tests Over the Period 1904 to 1950," by H. \. Gonnerman and William Lerch. Reprinted from Special Publication No. 127 pubh-hed b> American Society for Testing Materials. -"Studies of the Effect of Entrained Air on the Strength and Dura- bility of Concretes Made with Various Maximum Sizes of Aggregate, by Paul Klieger. Reprinted from Proceedings of the High\ Research Board, 31, 177 1 - Bulletin 41— "Effect of Settlement of Concrete on Results of Pull-Out Bond Tests," by Carl A. Mexzel, November, 1952. Bulletin 39 Bulletin 40 * i Bulletin 42 II An Investigation of Bond Anchorage and Related Factors in Rein- forced Concrete Beams," by Carl A. Menzel and William M. Wood-. November, 1952. Bulletin 4*-"Ten Year Report on the Long- lime Muav 01 umeni renuruiau,., in Concrete. •• bv Advisory I .mmittee of the Long-Time Study of Cement Pen'ornianc n ( acrete, R. F. Blanks, Chairman. Reprinted from Journal of the American Concrete Ins: March. 1953) ; Proceeding*. 49. 601 (1953). Bulletin 44— "The Reactions and Thermochemistry of Cement Hydration at Ordi- nary Temperature." by Harold H. SteinoTr. Reprinted from Third International S ponum on the Chemistry of Cement. London. Sept. 1952. Bulletin 4^— "Investigations of the Hydration Expansion Characteristics of Portland Cement. "• y H. F. Gonnbbma Wu. Ler. h. and Thoma- ML Uhitesidl June, 1953. Bulletin 46— "Theorv of Volume Changes in Hardened Portland Cement Paste During Freezing." by T. C. Powers and R. A. Helmuts. Reprinted from Proceedings of the Highway Research Board, 32 285 (1953). Bulletin 47— The Determination of Non-Evaporable Water in Hardened Portland Cement Paste," b L. E. Copeland and John < Hayes Reprinted fron - TM Bulletin So. 194. "0 (December. 1953). Bulletin 48— The Heats of Hydration of Tricalcium Silicate and beta-Dicalcium Silicate." by Stephen BRr.wu.-ER. T - C. Hates and W. r Ha- Reprinted from The Journal of Physical C'.emistry. SB. - ^ 1954). Bulletin 49 — "Void Spacing as a Basis for Producing Air-Entrained Concrete, by T. C Power- Reprinted from Journal of the American Concrete Institute May. 1954). Proceedings. 50. 741 (1954). Bulletin 4*) A— Discussion of the paper "Void Spacing as a Basis for Producing Air- Entrained Concrete," by J. E. Bacestrom. EL W. Burrows, \ E. \\ olx.- odoff and . jthor. T. C Power- Reprinted from Journal of the American Concrete Institute (Dec.. Part 2 I Pro- ceedings, 50 760-1 Bulletin 50 — "The Hydrates of Magnesium Perchlorate by L. E I pelaxd and R. H. Bragg. Reprinted from The Journal of Physical Chemistry 58. 1075 (1954 Bulletin 51 — "Determination of Sodium and Potassium Oxides in Portland Cement Raw Materials and Mixtures, and Similar Silicates by Flame Photom- em ." by C. L. 1 rd. Reprinted from A nalytical Chemistry 4b 1578 1954 Bulletin 52— "Self Desiccation in Portland Cement Pastes/' I L E. Cupelaad and Pi. H. Bragg. Reprinted from AS TM Bullet. N'o. 204 34 February. 1 Vl - Bulletin 53 — "Permeability of Portland Cement Pastes." by T.< • >wers L E Com l V I Bates and H. M. M \ Reprinted fit: Journal of th* American Concrete Insttiu November. 1954 Pro- ceeding*, 51 - (W - Bulletin 54 — "Some Observations on the Mechanics of Alkali- Aggregate Reaction," bv L S Brown Reprinted from ASTSi Bui No. 205 40 April. 1955). Bulletin 55— Wn Interpretation of Published Researches on the Alkali-Aggregate Reaction: Part 1 — The Chemical Reactions and Mechanism of Expan- sion; Part 2 — A Hypothesis Concerning Safe and Unsafe Reactions with Reactive Silica in Concrete," Powers and H . H ? ei> "R. % Reprinted from Journal of U \meriem ncret I istitu February and April. 1955 Proceeding* 51 " 'So Bulletin 56 — 'Comparison of Results of Three Methods for Determining Young - Modulus of Elasticity of Concrete/' by H. 1 Philleo. R -in ted from J jwnud o. -tricar. mcrei* InMitule (January. I Proce* 51 461 Bulletin 57 "Osmotic Studies and Hypothesis Concerning Alkali- Aggregate Re action," by ( rEORGE J. Verbeck and Charles Gramlich. Reprinted from Proceedings, American. Society for Testing Material*, 55, (1955). Bulletin 58— "Basic Considerations Pertaining to Freezing and Thawing Tests," by T. C. Powers Reprinted from Proceedings, American Society for Test Materials, 55, (l<~>v. Bulletin 59— "New Study on Reactions in Burning Cement Raw Materials," by L. A. Dahl. Reprinted from Rock Product*, 58, No. 5, 71; No. 6, 102; No. 7, 78 (1955). Bulletin 60— "Long- Time Study of Cement Performance in Concrete— Chapter 9. Correlation of the Results of Laboratory Tests with Field Performance Under Natural Freezing and Thawing Conditions," by F. H. Jackson. Reprinted from Journal of th I »,. an Com n '• Institute (October. 1955); Proceedings 52, 159 (1956). Bulletin 61 Bulletin 62 -"A Method for the Determination of the Cement Content of Plastic Concrete," by W. G. Himk and R. A. \\ ii.i.i.s. Reprinted from ASTM Bulletin No. 209. 37 (October. 1955). -"Investigation of the Franke Method of Determining Free Calcium Hydroxide and Free Calcium Oxide," by E. E. Pressler, Stephen Bri - naier ami 1). L. Kani m>. Reprinted from Analytical Chemistry, Vol. 00, p. 00, 1955. Bulletin 63— "Hydraulic Pressure in Concrete," by T. C. Powers. Reprinted from Proceeding* Ami lean Society of C - 81,74.' July, 1955 Bulletin 64 Bulletin 65 Bulletin 66 "The Freezing and Thawing Test," by T. C. Pow i rs Reprinted from ASTM R< port on Significance of Tests of Cor • ncrete Aggre- gates frd. Edition, 1955. 'The Stoichiometrv of the Hydration of Tricalcium Silicate at Room Temperature: I— Hydration in a Ball Mill; II— Hydration in a Paste Form," bv Stephen I'.kinu iii, L. E. Copeland and R EJ. Bragg. Reprinted from Th, Journal o) Pi col Chem > Vol. 60 p. 112 (January, 1" "Effect of Aggregate on Shrinkage of Concrete and Hypothesis Concern- ing Shrinkage, "by Gerald Pickett. Reprinted from Journal of th< biw Concrete Institu (January, 1956); Proceed- ings, 52, p. 581 1 1956).